Question

ABCD is a rectangle. Find the length of each diagonal.

AC=3(x-3)
BD=x+3

AC=___
BD=___

Answer 1

9

Explanation:

Ac = BD

3(x - 3) = x + 3 Distribute the 3

3x - 9 = x + 3 Subtract x from both sides

2x - 9 = 3 Add 9 to both sides

2x = 12 Divide both sides by 2

x = 6

Plug 6 back into either expression to solve for the side length

3(x - 3)

3(6-3)

3(3) = 9

or

x + 3

6 + 3 = 9

Answer 2

AC = BD = 9

Explanation:

the diagonals of a rectangle are congruent , then

AC = BD , that is

3(x - 3) = x + 3 ← distribute parenthesis on left side

3x - 9 = x + 3 ( subtract x from both sides )

2x - 9 = x + 3 ( add 9 to both sides )

2x = 12 ( divide both sides by 2 )

x = 6

Then

AC = 3(x - 3) = 3(6 - 3) = 3(3) = 9

BD = x + 3 = 6 + 3 = 9

that is AC = BD = 9